This week I wanted my Year 4 (8 and 9 year-old) class to have a good idea of factors and primes.

First, on Monday, we got the Cuisenaire rods out and looked at the "wall" of various numbers constructed from "layers" of the same colour:

I even liked the stencils they used and photographed them all for later use:

So on Tuesday I got four children to video/photograph the lesson, and here's an edit of what they captured:

I'm pleased that they've given me the chance to think the lesson over from other people's perspectives, and see some other things I might do. (Malke's also blogged about some of the issues here.)

What I take from it straight away is Christopher's suggestions about occupying the spaces, without markers, being conscious of the patterns from within, aware of the distances and directions of the other multiples of 3 or 7. Here the body is more intimately connected with the maths, it's not merely a means of adding to a big diagram, but actually takes its place

Malke mentions Seymour Papert. His book Mindstorms (pdf here) was my favourite during teacher training, and his turtle Logo programming has been incredibly influential. Among other things, with Logo geometry becomes something you walk through. It's this walking through the maths, or being a mathematical object even that gives a different and direct experience.

This probably needs to be done when the playground is peaceful and the weather comfortable. Another thing - one Malke and Christopher didn't mention - to focus attention, it might work well if some kind of game was involved at some point. It's amazing how well children concentrate in "Fizz Buzz". Maybe some kind of link could be made?

What did we do next?

On Wednesday we all coloured in the grid in the classroom, as is often done.

Doing it on screen is a good idea, as you can Ctrl Z any mistakes. (Those diagonal multiples of 3 are tricky!)

On Thursday we moved on to factor trees. I haven't photographed these yet, but you can see the results from when I did it last time here.

Any thoughts?

Ten has 4 layers: 10, 5, 2 and 1. Seven on the other hand only has 7 and 1.

This is enough to begin to make something clear: some numbers only have two layers. These numbers are primes, but I didn't say that, because the word "factors" was already new to some children in this lesson and I didn't want to give them more than one word in one go.

And - the Principle of Multiple Embodiment - I wanted to approach it from a different angle the next day.

Using the Sieve of Eratosthenes is a great way of sieving out all those numbers that are in another number's (apart from 1) times table, so that was the next step.

Last term a hundred square was painted in the playground. I had my eye on it right from the start.

My gut instinct is to use something like this rather than paper:

So on Tuesday I got four children to video/photograph the lesson, and here's an edit of what they captured:

I like the lesson (blogged here) and feel it achieved what I'd wanted from it for most of the children. I knew as it unfolded though that it had some weaknesses as well as some strengths.

#### Weaknesses

- Outdoors is distracting. This is a space in which the children normally do whatever kind of playing they choose. There are insects. There are planes going overhead. There's a lot to see that's not the maths. Another class came out half way through. I couldn't easily be face to face with the class and at the same time get them looking at the square and building the sieve.
- The cameras were a distraction - we hadn't used them before.
- I was being very directive; the children, though active for some of the time, didn't get much
*choice*in all this.

#### Strengths

- Although I think sitting still is a great thing, on balance I think we do too much of it at school. Our bodies and minds
**need movement**. - If I did it outdoors, I could
**do it again**indoors on screen and it would be different, not repetitive. - It's a
**performance**, and one different to our normal activities. Different means more chance of being memorable. - It's a
**spectacle**- one we can watch again, tweet, put on the blog, share with parents and other teachers. There's more chance of conversations developing.

And one did develop. Malke Rosenfeld, who with her Math in Your Feet brilliantly combines maths and dance, and beyond this takes a really wide interest in maths education, particularly when it involves the body, retweeted me. And then got into a tweet conversation about it with Christopher Danielson.

And Malke storified it:

And Malke storified it:

I'm pleased that they've given me the chance to think the lesson over from other people's perspectives, and see some other things I might do. (Malke's also blogged about some of the issues here.)

What I take from it straight away is Christopher's suggestions about occupying the spaces, without markers, being conscious of the patterns from within, aware of the distances and directions of the other multiples of 3 or 7. Here the body is more intimately connected with the maths, it's not merely a means of adding to a big diagram, but actually takes its place

*within*the diagram.

Malke mentions Seymour Papert. His book Mindstorms (pdf here) was my favourite during teacher training, and his turtle Logo programming has been incredibly influential. Among other things, with Logo geometry becomes something you walk through. It's this walking through the maths, or being a mathematical object even that gives a different and direct experience.

This probably needs to be done when the playground is peaceful and the weather comfortable. Another thing - one Malke and Christopher didn't mention - to focus attention, it might work well if some kind of game was involved at some point. It's amazing how well children concentrate in "Fizz Buzz". Maybe some kind of link could be made?

What did we do next?

On Wednesday we all coloured in the grid in the classroom, as is often done.

Doing it on screen is a good idea, as you can Ctrl Z any mistakes. (Those diagonal multiples of 3 are tricky!)

On Thursday we moved on to factor trees. I haven't photographed these yet, but you can see the results from when I did it last time here.

Any thoughts?

It took me the better part of the afternoon and evening but it was totally worth it -- thanks for giving me something to think about. I've needed a chance to clarify my thinking on all of this. So, here's my response: http://mathinyourfeet.blogspot.com/2013/10/an-object-to-think-with.html

ReplyDeleteThanks Simon!